Detailed analysis of steady-state kinetic studies on the mechanism of action of E. coli alkaline phosphatase has been completed. The flip-flop model is contrary to alternative substrate and product inhibition patterns. The effect of Tris on the k cat of this enzyme can be accounted for by the increased rate of dissociation of the Tris-phosphate product. A covalent intermediate of asparaginase, the aspartyl-enzyme, can be stabilized at acidic pH and low temperature. It is the first time that the elusive intermediate can be demonstrated. The kinetic mechanism of asparagine synthetase is shown to be consistent with a hybrid Uni Uni Bi Ter Ping-Pong-Theorell-Chance mechanism with abortive complexes. The "two-site" Ping-Pong mechanism can be ruled out. Mathematical proofs have been obtained for formulas for the rapid computation of King-Altman patterns. In addition, a method for calculating such patterns in the presence of irreversible steps has been established.